A measure of an object's tendency to align with a magnetic field, arising from its spin and orbital motion.The magnetic moment is a vector quantity that measures the strength and orientation of a particle's or object's tendency to align with an external magnetic field. It arises from two sources: the intrinsic spin of particles (like electrons) and their orbital motion around a nucleus or within a current loop. The magnetic moment is fundamental to understanding magnetism at all scales, from individual atoms to entire stars.
The concept of magnetic moment was developed in the 19th century, but its quantum treatment began with the work of Wolfgang Pauli and others in the 1920s. The precise measurement of the electron's magnetic moment (the anomalous magnetic moment) became a cornerstone of quantum electrodynamics and a test of the Standard Model.
For a charged particle, its spin creates a tiny circulating current, which generates a magnetic field — this is the spin magnetic moment. Similarly, an electron orbiting a nucleus produces a magnetic moment like a tiny current loop. In an external magnetic field, these moments experience a torque that tries to align them with the field. The magnitude of the magnetic moment determines how strongly the object interacts with the field, and its quantum nature means it can only take discrete orientations.
Magnetic moments are exploited in MRI imaging (where proton moments align in a magnetic field), in data storage (magnetic domains in hard drives), and in quantum sensing — for example, using nitrogen-vacancy centers in diamond to detect tiny magnetic fields from single spins.
The electron's magnetic moment is one of the most precisely measured quantities in physics, agreeing with theoretical predictions to better than one part in a trillion — one of the most accurate tests of any theory in science.
| H_{\text{HFI}} | variable | magnetic hyperfine interaction Hamiltonian — hamiltonian joule |
| \boldsymbol{\mu}_I | variable | nuclear magnetic moment — magnetic moment ampere square metre |
| \mathbf{A} | variable | hyperfine coupling tensor — tensor joule per ampere square metre |
| \mathbf{S} | variable | electron spin operator — spin operator |
| \cdot | operator | scalar product of vectors — dot product |


